"It is officially a wrap on @respectmovie wrap it up, it's done!" Hudson, 38, wrote in Saturday's post.
"To overwhelmed to get into it right now but words can't express how grateful I am to be chosen by the queen herself and to live out yet another dream! It was my honor, to honor the Queens request! The one and only Queen of soul #ArethaFranklin #respectMovie @liesltommy."
Known as the Queen of Soul, Franklin reportedly hand-picked Hudson to play her on the screen before she died in August 2018 at the age of 76.